Kent W. Hooper,<i> Ernst Barlach’s Literary and Visual Art. The Issue of Multiple Talent.</i>

Weisstein, Ulrich

doi:10.1515/arbi.1990.8.1.114

Cited by 16 publications

(21 citation statements)

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“…But latitude was first transformed by using the standard Mercator projection in order to make the two axes orthogonal and reduce any collinearity between latitude and longitude. For the most part, this operation created only slight changes in the estimates, although nontrivial shifts (greater than 2%) were experienced by both LATIT and DISTAN3 (Weisstein 2005). Compared with earlier models, the only noticeable difference that occurs among the factors is a reversal in the significance of factors 4 and 5, both of which are relatively marginal anyway.…”

Section: Resultsmentioning

confidence: 98%

Logistic Population Growth in the World's Largest Cities

Mulligan

2006

Geographical Analysis

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This article demonstrates that recent population growth in the world's largest cities has conformed to the general parameters of the logistic process. Using data recently provided by the United Nations, logistic population growth for 485 million-person cities is analyzed at 5-year intervals during 1950-2010, with the UN projections for 2015 adopted as upper limits. A series of ordinary least-squares regression models of increasing complexity are estimated on the pooled data. In one class of models, the logarithms of population proportions are specified to be linear in time, which is the standard approach, but in a second class of models those proportions are specified as being quadratic. The most complex models control logistic growth estimates for (i) city-specific effects (e.g., initial population), (ii) nation-specific effects (e.g., economic development, age distribution of population), and (iii) global coordinates (for unobserved effects). Moreover, the results are segregated according to each city's membership in four different growth clubs, which was an important finding of previous research.

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Section: Resultsmentioning

confidence: 98%

Logistic Population Growth in the World's Largest Cities

Mulligan

2006

Geographical Analysis

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“…The 'heptic collocation' method defined herein is identical to UH04's 'cubic collocation' method except that the expansion of f (η) in terms of the cubic-spline basis B i (η) is replaced by expansion in terms of H i (η) where, using the recursion formulae given in Weisstein (1999), H i (η) is the 7th-order spline-basis defined by…”

Section: (A) 'Heptic Collocation' Methodsmentioning

confidence: 99%

Comments on ‘A finite‐element scheme for the vertical discretization in the semi‐Lagrangian version of the ECMWF forecast model’ by A. Untch and M. Hortal (April B, 2004, 130, 1505–1530)

Staniforth¹,

Wood²

2005

Quart J Royal Meteoro Soc

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“…The Laplace equation has unique solutions for Dirichlet boundary conditions. () In our discretized context, this means that specifying Φ everywhere on the boundary should uniquely determine the a s. As a result, we expect the matrix [ A 1 ] to be invertible and write

({}, \frac{\partial normal Φ}{\partial n}) = false[A_{2} false] {false[A_{1} false]}^{- 1} ({}, normal Φ) = ([], S) ({}, normal Φ) .

Equation can be further split and written in the following block matrix form

({}, \begin{matrix} array {(\frac{\partial normalΦ}{\partial n})}_{tw} \\ array {(\frac{\partial normalΦ}{\partial n})}_{fs} \end{matrix}) = ([], \begin{matrix} array S_{11} & array S_{12} \\ array S_{21} & array S_{22} \end{matrix}) ({}, \begin{matrix} array {normalΦ}_{tw} \\ array {normalΦ}_{fs} \end{matrix})

where subscripts “tw” and “fs” represent the tank wall and the free surface, respectively. Using the boundary condition on the tank wall (Equation ) in Equation , we write

{normal Φ}_{tw} = - S_{11}^{- 1} S_{12} {normal Φ}_{fs}

whence

{((), \frac{\partial normal Φ}{\partial n})}_{fs} = ((), S_{22} - S_{21} S_{11}^{- 1} S_{12}) {normal Φ}_{}

…”

Section: Boundary Element Formulationmentioning

confidence: 99%

Overhead water tank shapes with depth-independent sloshing frequencies for use as TLDs in buildings

Bandyopadhyay

Maiti

Ghosh

et al. 2017

Struct Control Health Monit

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SummarySloshing water in the overhead water tank of a multi-storeyed building may be utilized to act as a tuned liquid damper for vibration control under wind and earthquake excitation. In conventional rectangular or circular water tanks, tuning presents difficulties as the sloshing frequency varies significantly with change in the depth of water in the tank. To address this issue, in this paper, we find shapes of tanks wherein the sloshing frequency is essentially independent of water depth over a large and useful range of water levels. Both two-dimensional as well as axisymmetric (three-dimensional) tank shapes are found. We use a direct boundary element method to find the sloshing frequencies in each case. In each case, a tentative simple analytical form for the tank shape is chosen with three free parameters, and these parameters are adjusted to obtain shapes where the first lateral sloshing frequency has negligible variation with water depth. For axisymmetric tanks, the circumferential (azimuthal) variation in field variables is restricted to the first harmonic, in the interest of lower computational effort. For both planar and axisymmetric cases, the working range of water depths is taken to be from 0.2 to 2 times the tank width. In both cases, the variation in first lateral sloshing mode frequency is found to be under 0.2% over the working range. In comparison, for constant width tanks such as the rectangular or circular ones, over the same range of water depths, the corresponding variation is more than 60 times greater.

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Kent W. Hooper, Ernst Barlach’s Literary and Visual Art. The Issue of Multiple Talent.

Cited by 16 publications

References 0 publications

Logistic Population Growth in the World's Largest Cities

Logistic Population Growth in the World's Largest Cities

Comments on ‘A finite‐element scheme for the vertical discretization in the semi‐Lagrangian version of the ECMWF forecast model’ by A. Untch and M. Hortal (April B, 2004, 130, 1505–1530)

Overhead water tank shapes with depth-independent sloshing frequencies for use as TLDs in buildings

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